The first step was an RSS feed of my friends page. I looked at the S1 one, but checkcookies didn't work (unfortunately - you'd think it would use Firefox's, and perhaps it will in a future version) and I wanted to be able to read protected posts. I realised that if I made an S2 style, I could use auth=digest to authenticate myself. So, I made an S2 style for RSS: http://www.livejournal.com/customize/advanced/layersource.bml?id=2870759&fmt=html. Paid users can copy the code from that layer into their own layer and use that as the basis for their own style - see the FAQ for info on creating a style.
Once you've got your style, you need to know its ID number. Then you can subscribe to your friends page at http://www.livejournal.com/users/exampleusername/friends/?s2id=XXXXXX. To see the full text of the post in plain-text, you'll need to check the "Display article summary" checkbox when you subscribe. If you want to read protected posts, you're going to need the latest nightly build of Thunderbird as the 0.9 release doesn't support digest authentication. Once you've got that, you can add &auth=digest to the URL. When you do, Thunderbird will ask you for your LJ username and password, which you can get it to save and then you're done!
If, like mine, your friends are a talkative bunch, you might also want to fetch entries more than 50 back. What you can do is to subscribe to http://www.livejournal.com/users/exampleusername/friends/?s2id=XXXXXX&skip=50. This will collect any items in the skipped back feed if it hasn't seen them before, so you don't miss out, but you don't get double copies of things either - nifty!
Edit Hmmm. The last paragraph was true when I tested it, I swear! But it doesn't seem to be true now for some reason - I'm getting double postings. If I work it out, I'll let you know.
Edit again Got it! It was caused by something I did when I was testing things - you shouldn't get any double posts if you set it up. It's worth noting though, that Thunderbird doesn't very thoroughly clean up when you delete a feed or account - you have to manually go to your profile and delete the folder to get it properly re-set.